Some remarks for a certain class of holomorphic functions at the boundary of the unit disc

Abstract

We consider a boundary version of the Schwarz Lemma on a certain class which isdenoted by K(alfa) . For the function f(z)=z+c2z2+....... which is defined in the unit disc Esuch that the function f (z) belongs to the class K(alfa) , we estimate from below the modulus of theangular derivative of the function ( )( )zf ' zf zat the boundary point b with ( ) = 1( ) 1bf ' bf b . Moreover,we get the Schwarz Lemma for the class K(alfa) . We also investigate some inequalities obtained interms of sharpness.